Topic

Repeated games with endogenous discounting

Abstract

In a symmetric
repeated game with standard preferences, there are no gains
from intertemporal trade. In fact, under a suitable
normalization of utility, the payoff set in the
repeated game is identical to that in the stage game. We show
that this conclusion may
no longer be true if preferences are recursive and stationary,
but not time separable. If
so, the players’ rates of time preference are no longer fixed,
but may vary endogenously,
depending on what transpires in the course of the game. This
creates opportunities for intertemporal trade, giving rise to
new and interesting dynamics. For example, the efficient
and symmetric outcome of a repeated prisoner’s dilemma may be
to take turns defecting,
even though the efficient and symmetric outcome of the stage
game is to cooperate. A
folk theorem shows that such dynamics can be sustained in
equilibrium if the players are
sufficiently patient.